Getal & Ruimte (12e editie) - vwo wiskunde B

'Rekenen met logaritmen'.

vwo wiskunde B 5.4 Logaritmen

Rekenen met logaritmen (8)

opgave 1

Bereken.

1p

a

\({}^{9}\!\log(81)\)

Logaritme (1)
00fi - Rekenen met logaritmen - basis - 0ms

a

\({}^{9}\!\log(81) = {}^{9}\!\log(9^{2}) = 2\)

1p

1p

b

\({}^{4}\!\log(4)\)

Logaritme (2)
00fj - Rekenen met logaritmen - basis - 0ms

b

\({}^{4}\!\log(4) = {}^{4}\!\log(4^{1}) = 1\)

1p

1p

c

\(\log(1\,000\,000)\)

Logaritme (3)
00fk - Rekenen met logaritmen - basis - 0ms

c

\(\log(1\,000\,000) = \log(10^{6}) = 6\)

1p

1p

d

\({}^{3}\!\log(\frac{1}{27})\)

Logaritme (4)
00fl - Rekenen met logaritmen - basis - 0ms

d

\({}^{3}\!\log(\frac{1}{27}) = {}^{3}\!\log(3^{-3}) = -3\)

1p

opgave 2

Bereken.

1p

a

\({}^{\frac{1}{4}}\!\log(\frac{1}{16})\)

Logaritme (5)
00fm - Rekenen met logaritmen - basis - 0ms

a

\({}^{\frac{1}{4}}\!\log(\frac{1}{16}) = {}^{\frac{1}{4}}\!\log(\frac{1}{4}^{2}) = 2\)

1p

1p

b

\({}^{\frac{1}{6}}\!\log(36)\)

Logaritme (6)
00fn - Rekenen met logaritmen - basis - 0ms

b

\({}^{\frac{1}{6}}\!\log({}^{\frac{1}{6}}\!\log(36)) = {}^{\frac{1}{6}}\!\log(\frac{1}{6}^{-2}) = -2\)

1p

1p

c

\({}^{4}\!\log(4 \sqrt{4})\)

Logaritme (7)
00fo - Rekenen met logaritmen - basis - 0ms

c

\({}^{4}\!\log(4 \sqrt{4}) = {}^{4}\!\log(4^{1} ⋅ 4^{\frac{1}{2}}) = {}^{4}\!\log(4^{1\frac{1}{2}}) = 1\frac{1}{2}\)

1p

1p

d

\({}^{3}\!\log(3^{2{,}4})\)

Logaritme (8)
00fp - Rekenen met logaritmen - basis - 0ms

d

\({}^{3}\!\log(3^{2{,}4}) = 2{,}4\)

1p

"